Aem Lect12

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Aem Lect12

  1. 1. DLVO theory: General DLVO (Derjaguin, Landau, Verwey, Overbeek) ♦ Electric Double Layer begins to interfere - electrostatic repulsion becomes significant ♦ Van der Waals Attraction In order to agglomerate, two particles on a collision course must have sufficient kinetic energy due to their velocity and mass to “jump over” the energy barrier Steric Stabilization - adsorption of polymer on particle surface prevent the particles from coming close enough for van der Waals attraction to cause flocculation For flocculation - mechanical bridging by long chain polymer enables flocculation in spite of the electrostatic forces that would normally make them repel each other. http://www.zeta-meter.com/ Advanced Electronic Ceramics I (2004) DLVO theory: General Potential Energy Curve Φtot = ΦR + ΦA Repulsion Born repulsion for atoms Double layer for colloids Attraction x-6 Van Der Waals for atoms D-2 for plates R/D for spheres Intermolecular force 1) Strong Bonding ionic bonding covalent bonding metallic bonding 2) Weak Bonding Van Der Waals Bonding 1. Debye (permanent dipole-induced dipole) 2. Keesom (permanent dipole-permanent dipole) 3. London (induced dipole-induced dipole) Advanced Electronic Ceramics I (2004)
  2. 2. Van Der Waals Bonding for atoms 1. Debye (permanent dipole-induced dipole) α1, α2: polarizability µ1: permanent dipole 2. Keesom (permanent dipole-permanent dipole) moment µ2: induced dipole moment x: distance from dipole 3. London (induced dipole-induced dipole) ΦVDWA = -βx-6 β: various interaction parameters(Jm6) Advanced Electronic Ceramics I (2004) Van Der Waals Attraction for plates As δ → ∞ δ δ D ΦR = [64nokTγo2/(κ)] exp (-κD) where γo = [exp(Zeϕo/2kT)-1]/[exp(Zeϕo/2kT)+1] (assumption D >> κ-1) ρNA/M : number of molecule per cubic centimeter (M= molecular weight) A: Hamaker constant (energy unit): Typical range : 10-20 ~ 10-19 J - a materials constant that depends on the dielectric properties of two materials and the intervening medium Advanced Electronic Ceramics I (2004)
  3. 3. Van Der Waals Attraction for spheres As R >> s 2R 2R s ΦR = [64πRnokTγo2/(κ2)] exp (-κs) where γo = [exp(Zeϕo/2kT)-1]/[exp(Zeϕo/2kT)+1] assumption: D>> κ-1 Advanced Electronic Ceramics I (2004) Van der Waals Attraction and Surface Tension - The difficulties of calculating β due to the lack of the information about the polarizability, permanent dipole orientation, chemical homogeneity of the surface - Evaluation of Hamaker constant via surface tension L WLL WLL: work of cohesion L L Advanced Electronic Ceramics I (2004)
  4. 4. Van der Waals Attraction and Surface Tension WLL = 2γL = ΦD=∞ - ΦD=do Do: intermolecular spacing γd: dispersion component of surface 2γL = A/(12πdo 2) A=24πγLdo2 tension when additional interaction besides London forces operates between the molecule A = 4πγddo2/(1.2) The estimation of Hamaker constant via the direct measurement of VDW forces as a function of separation using the displacement of sensitive spring and also from capacitance type measurement is not easy due to the external vibration and surface roughness Advanced Electronic Ceramics I (2004) Hamaker constant 1 When the materials interact across a liquid, their Hamaker constants decreases but remains high. Advanced Electronic Ceramics I (2004)
  5. 5. Hamaker constant 2 Flocculation occur + + 2 1 2 1 2 2 1 1 particle solvent Change in potential energy in above reaction ∆Φ = Φ11 + Φ22 -2Φ12 ΦA∝ A A212 = A11 + A22 -2A12 (A12 = (A11A22)1/2 : geometric mixing rule) ∴ A212 = (A111/2 - A221/2)2 1. Effective Hamaker constant A212 always >0 ( identical particles exert a net attraction due to van der Waals forces in a medium as well as under vacuum) 2. Embedding a particles in a medium generally diminishes the VDWA. 3. No interaction at A11=A22 - can be used to evaluate the A11 and A22 Advanced Electronic Ceramics I (2004) Repulsive and Attractive Potentials Both mode of interaction become weaker as the separation becomes larger. At sufficiently large spacing the particles exert no influence each other. For spherical particle r 2R 2R s Advanced Electronic Ceramics I (2004)
  6. 6. Repulsive and Attractive Potentials Kinetic of flocculation offer some clues as to the height of the maximum Metastable: possessing a degree of kinetic stability eventhough it lacks thermodynamic stability Advanced Electronic Ceramics I (2004) DLVO: Hamaker constant For plates Φtot = [64nokTγo2/(κ)] exp (-κd) -A/(12πd2) where γo = [exp(Zeϕo/2kT)-1]/[exp(Zeϕo/2kT)+1] (assumption D >> κ-1) A212↑ → VDWA [-A/(12πd2)]↓ Advanced Electronic Ceramics I (2004)
  7. 7. DLVO: ϕo For plates Φtot = [64nokTγo2/(κ)] exp (-κD) -A/(12πd2) where γo = [exp(Zeϕo/2kT)-1]/[exp(Zeϕo/2kT)+1] (assumption D >> κ-1) ϕo ↑ → γo ≈ 1 → ΦR ↑ sensitivity of the ΦR to the ϕo values decreases as ϕo values increases. For some system, ϕo values is adjustable by varying the concentration of potential determining ions. (remember Nernst equation) Advanced Electronic Ceramics I (2004) DLVO: κ For spheres Φtot = [64πRnokTγo2/(κ2)] exp (-κs) -AR/(12s) where γo = [exp(Zeϕo/2kT)-1] [exp(Zeϕo/2kT)+1] assumption: D>> κ-1 κ ↑ → ΦR ↓ Advanced Electronic Ceramics I (2004)
  8. 8. DLVO and CFC Advanced Electronic Ceramics I (2004) DLVO : summary Φtot = [64πRnokTγo2/(κ2)] exp (-κs) -AR/(12s) For spheres: Φtot = [64nokTγo2/(κ)] exp (-κD) -A/(12πd2) For plates: where γo = [exp(Zeϕo/2kT)-1]/[exp(Zeϕo/2kT)+1] (assumption D >> κ-1) 1. The higher the potential at the surface of particle(ϕo) - and therefore throughout the double layer - the larger repulsion(ΦR) between the particles will be. 2. The lower concentration of indifferent electrolyte, the longer is the distance from the surface before the repulsion drops significantly.(κ) 3. The larger Hamaker constant(A), the larger is the attraction between macroscopic bodies.(ΦA) Advanced Electronic Ceramics I (2004)

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